- Gerard Cornue?jols_ Javier Pen?a_ Reha Tu?tu?ncu? - Optimization Methods in Finance-Cambridge University Press
-Paolo Brandimarte - Numerical Methods in Finance and Economics_ A MATLAB-Based Introduction
-M. Choudhry, D. Moskovic, M. Wong: Fixed Income Markets
-B. Tuckman: Fixed Income Securities
The general purpose is to make the student familiar with some numerical solution methods and to use a specific modeling language by analysing a case study and preparing the required code.
The math prerequisite for the course is a basic knowledge of Linear Algebra.
Academic lessons and practical coding sessions
Type of Assessment
- Written exam
- Oral exam
- Description of the Investor's Objective: introduction to the stochastic dominance, definition of index of satisfaction and analysis of its properties, Introduction to the concept of Risk Aversion, propensity, and
neutrality, Introduction to the utility theory.
- Introduction/Description of the main portfolio theories: Mean-Variance (Markovitz ), Definition/study and construction of the efficient frontier, Description of the Capital Asset Pricing Model (CAPM), Description of the Consumption Capital Asset Pricing Model, Arbitrage Pricing Theory
- The Black-Litterman Model and the Entropy Pooling Approach.
- Basic theory of interest rates
- Introduction to optimization: classification, convex optimization
- Linear Programming: duality, Simplex method, Asset–Liability Management, sensitivity analysis, short term financing, Finding arbitrages;
- Quadratic Programming: Markovitz, Constraints, Applications in MATLAB, Portfolio Management;
- Dynamic Programming and Decision Processes;
- Bond Markets Essentials: The valuation of cash flows, Bond performance indexes, Clean and dirty prices of bonds;
- Forward rates: Forward rate agreements and Eurodollar futures, Forward rate agreements, Pricing FRA, Eurodollars futures contracts;
- Floating rate notes;
- The Italian government bond market;
- Coping with interest rate risk: The duration and convexity of cash flows;
- Swaps: Swap rates and bootstrapping, EONIA swaps, Multicurve approach and swap valuation after the financial crisis, Pricing and valuation of swaps using OIS discounting;